A unit of Lasting Forests
Sustained forests; sustained profits
evolving since March 30, 1999

of an Alternative Wildlife Resource Management

Variety as an alternative to Diversity

1. Diversity has many meanings.

2. There are over 1000 technical papers on the topic. It is not a new topic.

3. Biological diversity is shortened as biodiversity. Whether it means plants, animals, communities, genes or all of these must be determined from use and the context. It usually means animals but "phytodiversity" (as in phytomass) may help in some situations.

4. Diversity may mean:

1. Richness - the count of species (or taxa)
2. Variance (statistical)
3. Abundance - the number of organisms counted
4. Evenness - relations to a standard in which there are equal proportions of all counts in each species (or taxa)
5. Equitability - evenness endex relative to the maximum
6. Relative rarity - (as in Shannon-Weiner and Simpson index)

There are no clear standards and the "best" expression has not been selected

5. Diversity may be compared by

1. Taxa
2. Areas
3. Time
4. Treatment
5. Baseline-to-...some pre-condition
6. Behavior
7. Trophic groups
8. Sex
9. Age
10. Weight
11. Area(layers, size, shape, number of units)
12. Similarity
13. Genetic

The diversity of topics makes the concept almost impossible for the public or the courts to grasp and shifting groups can usually result in a change in a diversity index in an alternative direction

6. Diversity is a very diverse topic; at least 6x13 (the product of the 2 above lists) possible relations.

7. Richness, R, means the number of taxa. For example, one use might be to say: This area has 30; that one has 40. The one with 40 is more rich, more diverse, with greater biodiversity.

8. When a species becomes extinct, the area has a loss in richness. "Preserve species" is a richness slogan, only one aspect of diversity.

9. Taxonomic "lumpers" reduce richness; taxonomic "splitters" increase richness. Major change may occur with no physical changes in numbers of organisms in the field.

10. Genetics allows "splitting" of taxa or organisms to the individual; demes are analyzable; color phases (as in grouse or screech owls or squirrels) may also display diversity; subspecies (as in birds) may be appropriate analytical categories. There is no standard or criterion for judgement about such categories.

11. Abundance and richness are combined in the Simpson index.

Where the proportion in each ith species is p_i and means the processof summing all of the i's, then

V₁ = p_i²

The proportion of animals or plants in each ith species is used. Also called a dominance index, the value is 1.0 when all are in one species. This condition of all being in one species does not sound very diverse so the modified Simpson is usually used, namely

V₂ = 1.0 - V₁

12. The Shannon-Weiner index is frequently used. Named after the two people who independently developed the index, it is:

V₃= H = - ( p_ilog p_i)

Note the negative sign that is related to the logarithm of a proportion being negative, (it changes the negative to a positive value) thus, V₃ being made positive.

Because both abundance and the numbers of species may change, the index has no standard value or base figure against which a score can be obtained. Thus, the only uses are in knowledge that the larger the value, the "more diverse", at least the more evenly distributed.

The proportions are used as above. Logarithms with different bases, Log_e, log₁₀, and log₂, are all used. There is no best value; the more evenly distributed, the larger will be the value of V₃.

Several sets of proportions can give the same value of V₃. V₃ is a value in search of a meaning. It is called "average rarity."

13. Equitability, V₄, is a statistic comparing V₃ to the maximum value that would be obtained if all individuals in the sample studied were evenly distributed among the observed species present. It is relative Shannon-Weiner diversity. Using it results in a score or expression relative to a standard...but the meaning of the standard can shift with the season, sampling, etc. Diversity is a tough topic to grasp and, worse, to explain well in court or to use it as an objective or performance measure. The chief difficulty is that very different counts among species (say comparing before and after treatments) can result in identical numbers, the principle of equifinality.

14. V₂ and V₄ seem managerially useful.

15. Evenness, has an index

V₅ = V₃ / log R

It is another expression of evenness, as is V₃.

16.I think the ranked abundance (high to low) of species in a natural system will usually approach the negative exponential or "reversed J" distribution. How well an observed distribution fits this hypothesized distribution may be worth studying. The lack of evenness may be of much more interest than its presence. Only the top three numbers need to be analyzed by the field worker intent upon timely surveys and quick analyses. The negative rate will eventually be found to be significant for in the top most abundant life forms will there be integrated the energy and nutrients of the sampling period. The taxa, themselves are almost irrelevant. The forms are food for other organisms. They are merely temporary nitrogen, calcium, and energy pools, soon dissapated.

17. There are many published ways to produce an index to biodiversity. In preliminary studies that I have done with computer programs, a loss of one species can cause half these indices to increase, half to decrease. Arguing for biodiversity can be a useful political position because of this either/or as well as both/and condition.

18. The manager should pick a system performance measure, say "species X observations per hour along a transect", then develop a multiple regression, each independent variable being other species, values of each being abundance. Keep the abundance information separately so that effect of change in one can be observed on species. Stop using proportions since each species number is a function of the other numbers sampled, probably not the forces within the ecosystem.

19. Equifinality is a real problem if indices are used. Very different inputs from very different systems, when computed, can result in the same number, e.g., the "biodiversity". Avoid indices; work with regression analyses.

Assignment

1. Assume 3 recognized species. Sample sizes are 100 in each species (a total of 300 creatures). Compute a Shannon index.
2. Use a pesticide. Kill all of species 3. You now have 2 species, only 100 sampled in each. Compute a Shannon index. Campare the 2, with and without an insecticide treatment.
3. After the insecticide, species 1 and 2 increase mightly. You sample 500 of species 1, 500 of species 2. Compute a Shannon index. Compare. Write a brief comment.
4. When can stocking animals increase the diversity score? Decrease it?
5. In a sample of insects taken from a forest wildlife clearing, you have 56 species. The number is rank order were 1025, 873, and 311. The total sampled was only 2605 so most were in the top 3 species; the others were only traces and rare and almost unanalyzable. The difference between 18 and 11 as abundance of the 53rd and 54th insect in the sample no one knows! (even superior ecologists). Use a computer to get an approximate linear regression for the declining 3 top ranked numbers. What might this negative rate mean as a performance measure?

See The Trevey and its section on Variety.

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Last revision January 17, 2000.